Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.

Correct result:

V =  44790.6808 cm3

Solution:

a1=30 cm a2=12 cm s=41 cm n=6  S1=n 3/4 a12=6 3/4 302=1350 3 cm22338.2686 cm2 S2=n 3/4 a22=6 3/4 122=216 3 cm2374.123 cm2  x=s2(a1a2)2=412(3012)2=1357 cm36.8375 cm  h2=x a2/(a1a2)=36.8375 12/(3012)24.5583 cm h1=x+h2=36.8375+24.558361.3958 cm  V1=S1 h1/3=2338.2686 61.3958/347853.2914 cm3 V2=S2 h2/3=374.123 24.5583/33062.6107 cm3 V=V1V2=47853.29143062.6107=44790.6808 cm3



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